Hostname: page-component-745bb68f8f-d8cs5 Total loading time: 0 Render date: 2025-01-09T08:11:53.279Z Has data issue: false hasContentIssue false
  • English
  • Français

Pressure statistics and their scaling in high-Reynolds-number turbulent boundary layers

Published online by Cambridge University Press:  07 August 2007

Y. TSUJI ,
J. H. M. FRANSSON ,
P. H. ALFREDSSON  and
A. V. JOHANSSON
Y. TSUJI
Affiliation:
Department of Energy Engineering and Science, Nagoya University, Nagoya 464-8603, Japan
J. H. M. FRANSSON
Affiliation:
Linné Flow Centre, KTH Mechanics, SE-100 44 Stockholm, Sweden
P. H. ALFREDSSON
Affiliation:
Linné Flow Centre, KTH Mechanics, SE-100 44 Stockholm, Sweden
A. V. JOHANSSON
Affiliation:
Linné Flow Centre, KTH Mechanics, SE-100 44 Stockholm, Sweden
Get access Rights & Permissions [Opens in a new window]

Abstract

Pressure fluctuations are an important ingredient in turbulence, e.g. in the pressure strain terms which redistribute turbulence among the different fluctuating velocity components. The variation of the pressure fluctuations inside a turbulent boundary layer has hitherto been out of reach of experimental determination. The mechanisms of non-local pressure-related coupling between the different regions of the boundary layer have therefore remained poorly understood. One reason for this is the difficulty inherent in measuring the fluctuating pressure. We have developed a new technique to measure pressure fluctuations. In the present study, both mean and fluctuating pressure, wall pressure, and streamwise velocity have been measured simultaneously in turbulent boundary layers up to Reynolds numbers based on the momentum thickness Rθ ≃ 20000. Results on mean and fluctuation distributions, spectra, Reynolds number dependence, and correlation functions are reported. Also, an attempt is made to test, for the first time, the existence of Kolmogorov's -7/3 power-law scaling of the pressure spectrum in the limit of high Reynolds numbers in a turbulent boundary layer.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 585 , 25 August 2007 , pp. 1 - 40
Copyright
Copyright © Cambridge University Press 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Abe, H., Matsuo, Y. & Kawamura, H. 2005 A DNS study of Reynolds-number dependence on pressure fluctuations in a turbulent channel flow. In Proc. Fourth Intl Symp. on Turbulence and Shear Flow Phenomena, Williamsburg, VA USA, 27–29 June, pp. 189–194.Google Scholar
Albertson, J. D., Katul, G. G., Parlange, M. B. & Eichinger, W. E. 1998 Spectral scaling of static pressure fluctuations in the atmospheric surface layer: The interaction between large and small scales. Phys. Fluids 10, 1725–1732.CrossRefGoogle Scholar
Alfredsson, P. H. & Johansson, A. V. 1984 Time scale in turbulent channel flow. Phys. Fluids 27, 1974–1980.CrossRefGoogle Scholar
Alfredsson, P. H., Johansson, A. V. & Kim, J. 1988 Turbulence production near walls: the role of flow structures with spanwise asymmetry. Studying Turbulence Using Numerical Simulation Databases – II. Proc. 1988 Summer program, Center for Turbulence Research, Report CTR-S88.Google Scholar
Alvelius, K. & Johansson, A. V. 2000 Les computations and comparison with kolmogorov theory for two-point pressure-velocity correlations and structure functions for globally anisotropic turbulence. J. Fluid Mech. 403, 22–36.CrossRefGoogle Scholar
Arad, I., Dhruva, B., Kurien, S., L'vov, V. S., Procaccia, I. & Sreenivasan, K. R. 1998 Extraction of anisotropic contribution in turbulent flows. Phys. Rev. Lett. 81, 5330–5333.CrossRefGoogle Scholar
Batchelor, G. K. 1951 Pressure fluctuations in isotropic turbulence. Proc. Camb. Phil. Soc. 47, 359–374.CrossRefGoogle Scholar
Bradshaw, P. 1967 a Inactive motion and pressure fluctuation in turbulent boundary layers. J. Fluid Mech. 30, 241–258.CrossRefGoogle Scholar
Bradshaw, P. 1967 b The turbulence structure of equilibrium boundary layers. J. Fluid Mech. 29, 625–645.CrossRefGoogle Scholar
Bull, M. K. 1996 Wall-pressure fluctuations beneath turbulent boundary layers: Some reflections on forty years of research. J. Sound Vib. 190, 299–315.CrossRefGoogle Scholar
Cadot, O., Douady, S. & Couder, Y. 1995 Characterization of the low-pressure filaments in a three-dimensional turbulent shear flow. Phys. Fluids 7, 630–646.CrossRefGoogle Scholar
Cao, N., Chen, S. & Doolen, G. D. 1999 Statistics and structures of pressure in isotropic turbulence. Phys. Fluids 11, 2235–2250.CrossRefGoogle Scholar
Chue, S. H. 1975 Pressure probes for fluid measurement. Prog. Aerospace Sci. 16, 147–223.CrossRefGoogle Scholar
Corcos, G. M. 1963 Resolution of pressure in turbulence. J. Acoustic. Soc. Am. 35, 192–199.CrossRefGoogle Scholar
Eckelmann, H. 1989 A review of knowledge of pressure fluctuations. In Proc. 1988 Zoran Zaric Memorial Conference, Dubrovnik, Croatia (ed. Kline, S. J. & Afgan, N. H.), pp. 328–347.Google Scholar
Eggels, J. G. M., Unger, F., Weiss, M. H., Westerweel, J., Adrian, R. J., Friedrich, R. & Nieuwstadt, F. T. M. 1994 Fully developed turbulent pipe flow: a comparison between direct numerical simulation and experiment. J. Fluid Mech. 268, 175–209.CrossRefGoogle Scholar
Elliot, J. A. 1972 Microscale pressure fluctuations measured within the lower atmospheric boundary layer. J. Fluid Mech. 53, 351–383.CrossRefGoogle Scholar
Farabee, T. M. & Casarella, M. J. 1986 Measurements of fluctuating wall pressure for separated reattached boundary-layer flows. Trans. ASME: J. Vib. Acoust. 108, 301–307.Google Scholar
Farabee, T. M. & Casarella, M. J. 1991 Spectral features of wall pressure fluctuations beneath turbulent boundary layers. Phys. Fluids 3, 2410–2420.CrossRefGoogle Scholar
Fernholz, H. F. & Finley, P. J. 1996 The incompressible zero-pressure-gradient turbulent boundary layer: An assessment of the data. Prog. Aerospace Sci. 32, 245–311.CrossRefGoogle Scholar
Gedney, C. J. & Leehey, P. 1991 Wall pressure fluctuations during transition on a flat plate. Trans. ASME: J. Vib. Acoust. 113, 255–266.Google Scholar
George, W. K., Beuther, P. D. & Arndt, R. E. A. 1984 Pressure spectra in turbulent free shear flows. J. Fluid Mech. 148, 155–191.CrossRefGoogle Scholar
Goldstein, S. A. 1936 A note on measurement of total head and static pressure in a turbulent stream. Proc. R. Soc. Lond. A 155, 570–575.Google Scholar
Gotoh, T. & Fukayama, D. 2001 Pressure spectrum in homogeneous turbulence. Phys. Rev. Lett. 86, 3775–3778.CrossRefGoogle ScholarPubMed
Gotoh, T. & Rogallo, R. S. 1999 Intermittency and scaling of pressure at small scales in forced isotropic turbulence. J. Fluid Mech. 396, 257–285.CrossRefGoogle Scholar
Gravante, S. P., Naguib, A. M., Wark, C. E. & Nagib, H. M. 1998 Characterization of the pressure fluctuations under a fully developed turbulent boundary layer. AIAA J. 36, 1808–1816.CrossRefGoogle Scholar
Heisenberg, W. 1948 Zür Statistischen Theorie der Turbulenz. Z. Phys. 124, 628–657.CrossRefGoogle Scholar
Hill, R. J. 2002 Scaling of acceleration in locally isotropic turbulence. J. Fluid Mech. 452, 361–370.CrossRefGoogle Scholar
Hill, R. J. & Wilczak, J. M. 1995 Pressure stucture functions and spectra for locally isotropic turbulence. J. Fluid Mech. 296, 247–269.CrossRefGoogle Scholar
Hinze, J. O. 1975 Turbulence. McGraw-Hill.Google Scholar
Iida, A., Otaguro, T., Kato, C. & Shimode, S. 1998 Analysis of aerodynamic sound source with measurement of static-pressure fluctuation. JSME 64, 2057–2064 (in Japanese).CrossRefGoogle Scholar
Inoue, E. 1951 The application of the turbulence theory to the large-scale atmospheric phenomena. Geophys. Mag. 23, 1–14.Google Scholar
Ishihara, T., Kaneda, Y., Yokokawa, M., Itakura, K. & Uno, A. 2003 Spectra of energy dissipation, enstropy and pressure by high-resolution direct numerical simulations of turbulence in a periodic box. J. Phys. Soc. Japan 72, 983–986.CrossRefGoogle Scholar
Jeong, J., Hussain, F., Schoppa, W. & Kim, J. 1997 Coherent structures near the wall in a turbulent channel flow. J. Fluid Mech. 332, 185–214.CrossRefGoogle Scholar
Johansson, A. V., Alfredsson, P. H. & Kim, J. 1991 Evolution and dynamics of shear-layer structures in near-wall turbulence. J. Fluid Mech. 224, 579–599.CrossRefGoogle Scholar
Jones, B. G., Adrian, R. J., Nithiandan, C. K. & Planchon, H. P. 1979 Spectra of turbulent static pressure fluctuation in jet mixing layers. AIAA J. 17, 449–457.CrossRefGoogle Scholar
JSME 1985 JSME Data Book: Flow Measurement. The Japan Society of Mechanical Engineering.Google Scholar
Keith, W. L., Hurdis, D. A. & Abraham, B. M. 1992 A comparison of turbulent boundary layer wall-pressure spectra. Trans. ASME: J. Fluids Engng 114, 338–347.Google Scholar
Kida, S. & Miura, H. 1998 Identification and analysis of vortical structures? Eur. J. Mech.B-Fluids 17, 471–488.CrossRefGoogle Scholar
Kim, J. 1989 On the structure of pressure fluctuations in simulated turbulent channel flow. J. Fluid Mech. 205, 421–451.CrossRefGoogle Scholar
Klewicki, J. C., Perkins, B. F. & Metzge, M. M. 2005 Wall pressure statistics in a high reynolds number turbulent boundary layer. In Proc. Fourth Intl Symp. on Turbulence and Shear Flow Phenomena, Williamsburg, VA USA, 27–29 June (ed. Humphrey, J. A. C., Gatski, T. B., Eaton, J. K., Friedrich, R., Kasagi, N. & Leschziner, M. A.), pp. 21–26.Google Scholar
Kobashi, Y. 1957 Measurements of pressure fluctuation in the wake of cylinder. J. Phys. Soc. Japan 12, 533–543.CrossRefGoogle Scholar
Kobashi, Y. & Ichijo, M. 1986 Wall pressure and its relation to turbulent structure of a boundary layer. Exps. Fluids 4, 49–55.CrossRefGoogle Scholar
Kobashi, Y., Komoda, H. & Ichijo, M. 1984 Wall pressure fluctuation and the turbulence structure of a boundary layer. In Turbulence and Chaotic Phenomena in Fluids (ed. Tatsumi, T.), pp. 461–466. Elsevier.Google Scholar
Kobashi, Y., Kono, N. & Nishi, T. 1960 Improvement of a pressure pickup for the measurements of turbulence characteristics. J. Aero/Space Sci. 27, 149–151.CrossRefGoogle Scholar
Kurien, S., L'vov, V. S., Procaccia, I. & Sreenivasan, K. R. 2000 Scaling structure of the velocity statistics in atmospheric boundary layers. Phys. Rev. E 61, 407–421.Google ScholarPubMed
La Porta, A., Voth, G. A., Crawford, A. M., Alexander, J. & Bodenschatz, E. 2001 Fluid particle accelerations in fully developed turbulence. Nature 409, 1017–1019.CrossRefGoogle ScholarPubMed
Lindgren, B. 2002 Flow facility design and experimental studies of wall-bounded turbulent shear-flow. PhD thesis, TRITA-MEK Tech. Rep. 2002:16, Dept. Mech., KTH, Stockholm, Sweden.Google Scholar
Lindgren, B., Johansson, A. V. & Tsuji, Y. 2004 Universality of probability density distributions in the overlap region in high reynolds number turbulent boundary layer. Phys. Fluids 16, 2587–2591.CrossRefGoogle Scholar
LÖfdahl, L. & Gad-el-Hak, M. 1999 MEMS-based pressure and shear stress sensors for turbulent flow. Meas. Sci. Technol. 10, 665–686.CrossRefGoogle Scholar
Lueptow, R. M. 1995 Transducer resolution and the turbulent wall pressure spectrum. J. Acoust. Soc. Am. 97, 370–378.CrossRefGoogle Scholar
Monin, M. S. & Yaglom, A. M. 1971 Statistical Fluid Mechanics, Vol. 2. The MIT Press.Google Scholar
Moser, R. D., Kim, J. & Mansour, N. N. 1999 Direct numerical simulation of turbulent channel flow up to Reτ = 590. Phys. Fluids 11, 943–945.CrossRefGoogle Scholar
Naka, Y., Omori, T., Obi, S. & Masuda, S. 2005 Experimental study on velocity-pressure correlation in turbulent mixing layer out of equilibrium state. In Proc. Fourth Intl Symp. on Turbulence and Shear Flow Phenomena, Williamsburg, VA USA, 27–29 June (ed. Humphrey, J. A. C., Gatski, T. B., Eaton, J. K., Friedrich, R., Kasagi, N. & Leschziner, M. A.), pp. 1125–1130.Google Scholar
Nepomuceno, H. G. & Lueptow, R. M. 1997 Pressure and shear stress measurements at the wall in a turbulent boundary layer on a cylinder. Phys. Fluids 9, 2732–2739.CrossRefGoogle Scholar
Obukhov, A. M. 1949 Pressure fluctuations in a turbulent flow. Dokl. Akad. Nauk SSSR 66, 17–20.Google Scholar
Obukhov, A. M. & Yaglom, A. M. 1951 The microstructure of turbulent flow. NACA TM 1350Google Scholar
Österlund, J. M. 1999 Experimental studies of zero pressure-gradient turbulent boundary layer flow. PhD thesis, TRITA-MEK Tech. Rep. 1999:16, Dept. Mech., KTH, Stockholm, Sweden.Google Scholar
Österlund, J. M., Johansson, A. V., Nagib, H. M. & Hites, M. H. 2000 A note on the overlap region in turbulent boundary layers. Phys. Fluids 12, 1–4.CrossRefGoogle Scholar
Panton, R. L., Goldman, A. L., Lowery, R. L. & Reischman, M. M. 1980 Low-frequency pressure fluctuations in axisymmetric turbulent boundary layers. J. Fluid Mech. 97, 299–319.CrossRefGoogle Scholar
Panton, R. L. & Linebarger, J. H. 1974 Wall pressure spectra calculations for equilibrium boundary layers. J. Fluid Mech. 65, 261–287.CrossRefGoogle Scholar
Perry, A. E., Henbest, S. M. & Chong, M. S. 1986 A theoretical and experimental study of wall turbulence. J. Fluid Mech. 165, 163–199.CrossRefGoogle Scholar
Pumir, A. 1994 A numerical study of pressure fluctuations in three-dimensional, incompressible, homogeneous, isotropic turbulence. Phys Fluids 6, 2071–2083.CrossRefGoogle Scholar
Schewe, G. 1983 On the structure and resolution of wall-pressure fluctuations associated with turbulent boundary-layer flow. J. Fluid Mech. 134, 311–328.CrossRefGoogle Scholar
Shaw, R. 1960 The influence of hole dimensions on static pressure measurements. J. Fluid Mech. 9, 550–556.CrossRefGoogle Scholar
Shen, X. & Warhaft, Z. 2000 The anisotropy of the small scale structure in high reynolds number turbulent shear flow. Phys. Fluids 12, 2976–2989.CrossRefGoogle Scholar
Skote, M. 2001 Studies of turbulent boundary layer flow through direct numerical simulation. PhD thesis, TRITA-MEK Tech. Rep. 2001:01, Dept. Mech., KTH, Stockholm, Sweden.Google Scholar
Spalart, P. R. 1988 Direct simulation of a turbulent boundary layer up to Rθ J. Fluid Mech. 187, 61–98.CrossRefGoogle Scholar
Sreenivasan, K. R. & Antonia, R. A. 1997 The phenomenology of small-scale turbulence. Annu. Rev. Fluid Mech. 29, 435–472.CrossRefGoogle Scholar
Tanifuji, N., Ichijo, M., Iida, S. & Kobashi, Y. 1986 Coherent structures in fully developed turbulent pipe flow. Bull. JSME 29, 1156–1162.CrossRefGoogle Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press.Google Scholar
Toyoda, K., Okamoto, T. & Shirahama, Y. 1993 Eduction of vortical structures by pressure measurements in noncircular jet. Fluid Mech. Applics. 21, 125–136.Google Scholar
Tsuji, Y. 2003 Large-scale anisotropy effect on small-scale statistics over rough wall turbulent boundary layers. Phys. Fluids 12, 3816–3828.CrossRefGoogle Scholar
Tsuji, Y., Fransson, J. H. M., Alfredsson, P. H. & Johansson, A. V. 2005 a Pressure statistics in high-Reynolds number turbulent boundary layer. In Proc. Fourth Intl Symp. on Turbulence and Shear Flow Phenomena, Williamsburg, VA USA, 27–29 June (ed. Humphrey, J. A. C., Gatski, T. B., Eaton, J. K., Friedrich, R., Kasagi, N. & Leschziner, M. A.), pp. 27–32.Google Scholar
Tsuji, Y. & Ishihara, T. 2003 Similarity scaling of pressure fluctuation in turbulence. Phys. Rev. E 68, 026309.Google ScholarPubMed
Tsuji, Y. & Ishihara, T. 2006 Pressure statistics in turbulence. In IUTAM Symposium on Elementary Vortices and Coherent Structures: Significance in Turbulence Dynamics, Kyoto Japan, 26–28 October, 2004, pp. 163–170. Springer.CrossRefGoogle Scholar
Tsuji, Y., Lindgren, B. & Johansson, A. V. 2005 b Self-similar profile of probability density functions in zero-pressure gradient turbulent boundary layers. Fluid Dyn. Res. 37, 293–316.CrossRefGoogle Scholar
Vedula, P. & Yeung, P. K. 1999 Similarity scaling of acceleration and pressure statistics in numerical simulation of isotropic turbulence. Phys. Fluids 11, 1208–1220.CrossRefGoogle Scholar
Voth, G. A., Satyanarayan, K. & Bodenschatz, E. 1998 Lagrangian acceleration measurements at large Reynolds numbers. Phys. Fluids 10, 2268–2280.CrossRefGoogle Scholar
Willmarth, W. W. 1975 Pressure fluctuations beneath turbulent boundary layers. Annu. Rev. Fluid Mech. 7, 13–38.CrossRefGoogle Scholar
Yaglom, A. M. 1949 Acceleration field in a turbulent flow. Dokl. Akad. Nauk SSSR 67, 795–798.Google Scholar